Areas of central London, including Soho, Covent Garden and Leicester Square, were left in darkness when the power cut began at around 7.30pm.
A UK Power Networks spokesman said there were various faults in the area. Power was restored by 10pm.
A message posted on Miss Saigon's official Twitter account apologised for the cancellation of the performance and advised ticket holders to contact their point of purchase to arrange a refund or ticket exchange.
Apologies for this evening's cancellation due to a power cut in Soho. Ticket holders, pls contact point of sale for refunds/ticket exchange.— Miss Saigon (@MissSaigonUK) October 21, 2015
Really sorry for everyone who came to our cancelled show tonight @MissSaigonUK due to power failure. I hope you all get sorted out.— Jon Jon Briones (@JonJonBriones) October 22, 2015
Jon Jon Briones, who stars in the production as The Engineer, added: "Really sorry for everyone who came to our cancelled show tonight @MissSaigonUK due to power failure. I hope you all get sorted out."
Boublil and Schönberg’s musical runs at the Prince Edward Theatre until 27th February 2016, having opened in May 2014.
The current cast also includes Eva Noblezada as ‘Kim’, Chris Peluso as ‘Chris’, WEF Award winner Carolyn Maitland as ‘Ellen’, Hugh Maynard as ‘John’, Sangwoong Jo as ‘Thuy’ and Natalie Mendoza as ‘Gigi’.